Maybe it's because Naruto has some sort of special connection or resemblance to the Kyuubi that Kushina notices. For example, Naruto might display some of the Kyuubi's power characteristics in an obvious way that makes Kushina jump to that conclusion.
One possible plotline could be Naruto growing up with a sense of deep abandonment and having to face the world alone. This could lead to him having a much more cynical view of life. He might struggle more with controlling the Kyuubi's power as he has no guidance from Kushina. Another aspect could be his relationships with other characters like Iruka or Sasuke being different. Without Kushina's love, he may be more desperate for any form of connection.
In this type of fanfiction, the story could also focus on how the village might react differently to Naruto. Without Kushina's presence, which could potentially have been a positive influence, Naruto might face more hostility. His struggle to fit in and gain acceptance could be more arduous, and this could be what drives him to the brink of insanity. Maybe he would develop a more jaded view of the world and the people in it.
Fanfiction about Naruto being abandoned by Minato and Kushina can also be a way to explore different power - up scenarios. Since he doesn't have the emotional support from his parents, he might be forced to seek power in other ways, which could lead to a Naruto with a very different set of skills and abilities compared to the original series.
His character development would likely be much darker. He would lack the initial source of love and support that Kushina was supposed to provide. This could make him more distrustful of others. For example, he might not be as quick to form bonds with his teammates in the same way he did in the original story.
Well, in fanfictions about Naruto, Kushina and Kyuubi, their relationships can vary greatly. Some fanfictions might focus on how Naruto inherits not only the Kyuubi's power but also some of Kushina's traits. For example, Kushina was known for her strong will, and Naruto might be shown to have an even stronger will because of her influence and the presence of the Kyuubi. The Kyuubi could be portrayed as a protector of Naruto in a sense, especially when it comes to threats that are related to Naruto's family history. And Kushina could be like a spiritual guide for Naruto when it comes to dealing with the Kyuubi's power.
One possible reason could be some sort of dark force influencing Kushina's mind. Maybe she was under a powerful genjutsu that made her think she had to abandon Naruto for his own safety, even though it was a false perception.
I'm not sure specifically as there could be many different plots in such a fanfiction. It might involve Naruto having some god - like powers but being rejected or abandoned by his mother Kushina for various reasons, perhaps due to fear of his power or some dark influence.
Well, in such a fanfiction, Naruto might initially be filled with anger and confusion. He may have a harder time connecting with his peers in the village. As he gets older, he could start to piece together the events that led to Kushina's abandonment. Maybe there was some dark force or misunderstanding that caused it. This could lead to a whole series of adventures where he tries to set things right or find a new family in the form of his friends and mentors.
The fanfiction would also change the relationship dynamics in the story. For instance, Naruto's relationship with his father Minato would be more complex as he might also feel some resentment towards Minato for not preventing Kushina from leaving. It could also affect how Naruto views family in general, making him more cynical or desperate for family love.